Data Mining: Data. Lecture Notes for Chapter 2. Introduction to Data Mining

Transcription

1 Data Mining: Data Lecture Notes for Chapter 2 Introduction to Data Mining by Tan, Steinbach, Kumar

2 10 What is Data? Collection of data objects and their attributes Attributes An attribute is a property or characteristic of an object Examples: eye color of a person, temperature, etc. Attribute is also known as variable, field, characteristic, or feature A collection of attributes describe an object Object is also known as record, point, case, sample, entity, or instance Objects Tid Refund Marital Status Taxable Income 1 Yes Single 125K No 2 No Married 100K No 3 No Single 70K No 4 Yes Married 120K No Cheat 5 No Divorced 95K Yes 6 No Married 60K No 7 Yes Divorced 220K No 8 No Single 85K Yes 9 No Married 75K No 10 No Single 90K Yes

3 Attribute Values Attribute values are numbers or symbols assigned to an attribute Distinction between attributes and attribute values Same attribute can be mapped to different attribute values Example: height can be measured in feet or meters Different attributes can be mapped to the same set of values Example: Attribute values for ID and age are integers But properties of attribute values can be different ID has no limit but age has a maximum and minimum value

4 Measurement of Length The way you measure an attribute is somewhat may not match the attributes properties. 5 7 A B C 3 D 10 4 E 15 5

5 Types of Attributes There are different types of attributes Nominal Ordinal Interval Ratio Examples: ID numbers, eye color, zip codes Examples: rankings (e.g., taste of potato chips on a scale from 1-10), grades, height in {tall, medium, short} Examples: calendar dates, temperatures in Celsius or Fahrenheit. Examples: temperature in Kelvin, length, time, counts

6 Properties of Attribute Values The type of an attribute depends on which of the following properties it possesses: Distinctness: = Order: < > Addition: + - Multiplication: * / Nominal attribute: distinctness Ordinal attribute: distinctness & order Interval attribute: distinctness, order & addition Ratio attribute: all 4 properties

7 Attribute Type Description Examples Operations Nominal The values of a nominal attribute are just different names, i.e., nominal attributes provide only enough information to distinguish one object from another. (=, ) zip codes, employee ID numbers, eye color, sex: {male, female} mode, entropy, contingency correlation, 2 test Ordinal The values of an ordinal attribute provide enough information to order objects. (<, >) hardness of minerals, {good, better, best}, grades, street numbers median, percentiles, rank correlation, run tests, sign tests Interval For interval attributes, the differences between values are meaningful, i.e., a unit of measurement exists. (+, - ) calendar dates, temperature in Celsius or Fahrenheit mean, standard deviation, Pearson's correlation, t and F tests Ratio For ratio variables, both differences and ratios are meaningful. (*, /) temperature in Kelvin, monetary quantities, counts, age, mass, length, electrical current geometric mean, harmonic mean, percent variation

8 Attribute Level Transformation Comments Nominal Any permutation of values If all employee ID numbers were reassigned, would it make any difference? Ordinal Interval An order preserving change of values, i.e., new_value = f(old_value) where f is a monotonic function. new_value =a * old_value + b where a and b are constants An attribute encompassing the notion of good, better best can be represented equally well by the values {1, 2, 3} or by { 0.5, 1, 10}. Thus, the Fahrenheit and Celsius temperature scales differ in terms of where their zero value is and the size of a unit (degree). Ratio new_value = a * old_value Length can be measured in meters or feet.

9 Discrete and Continuous Attributes Discrete Attribute Has only a finite or countably infinite set of values Examples: zip codes, counts, or the set of words in a collection of documents Often represented as integer variables. Note: binary attributes are a special case of discrete attributes Continuous Attribute Has real numbers as attribute values Examples: temperature, height, or weight. Practically, real values can only be measured and represented using a finite number of digits. Continuous attributes are typically represented as floating-point variables.

10 Types of data sets Record Data Matrix Document Data Transaction Data Graph World Wide Web Molecular Structures Ordered Spatial Data Temporal Data Sequential Data Genetic Sequence Data

11 Important Characteristics of Structured Data Dimensionality Curse of Dimensionality Sparsity Only presence counts Resolution Patterns depend on the scale

12 10 Record Data Data that consists of a collection of records, each of which consists of a fixed set of attributes Tid Refund Marital Status Taxable Income Cheat 1 Yes Single 125K No 2 No Married 100K No 3 No Single 70K No 4 Yes Married 120K No 5 No Divorced 95K Yes 6 No Married 60K No 7 Yes Divorced 220K No 8 No Single 85K Yes 9 No Married 75K No 10 No Single 90K Yes

13 Data Matrix If data objects have the same fixed set of numeric attributes, then the data objects can be thought of as points in a multi-dimensional space, where each dimension represents a distinct attribute Such data set can be represented by an m by n matrix, where there are m rows, one for each object, and n columns, one for each attribute Projection of x Load Projection of y load Distance Load Thickness

14 Document Data Each document becomes a `term' vector, each term is a component (attribute) of the vector, the value of each component is the number of times the corresponding term occurs in the document. season timeout lost wi n game score ball pla y coach team Document Document Document

15 Transaction Data A special type of record data, where each record (transaction) involves a set of items. For example, consider a grocery store. The set of products purchased by a customer during one shopping trip constitute a transaction, while the individual products that were purchased are the items. TID Items 1 Bread, Coke, Milk 2 Beer, Bread 3 Beer, Coke, Diaper, Milk 4 Beer, Bread, Diaper, Milk 5 Coke, Diaper, Milk

16 Graph Data Examples: Generic graph and HTML Links <a href="papers/papers.html#bbbb"> Data Mining </a> <li> <a href="papers/papers.html#aaaa"> Graph Partitioning </a> <li> <a href="papers/papers.html#aaaa"> Parallel Solution of Sparse Linear System of Equations </a> <li> <a href="papers/papers.html#ffff"> N-Body Computation and Dense Linear System Solvers

17 Chemical Data Benzene Molecule: C 6 H 6

18 Ordered Data Sequences of transactions Items/Events An element of the sequence

19 Ordered Data Genomic sequence data GGTTCCGCCTTCAGCCCCGCGCC CGCAGGGCCCGCCCCGCGCCGTC GAGAAGGGCCCGCCTGGCGGGCG GGGGGAGGCGGGGCCGCCCGAGC CCAACCGAGTCCGACCAGGTGCC CCCTCTGCTCGGCCTAGACCTGA GCTCATTAGGCGGCAGCGGACAG GCCAAGTAGAACACGCGAAGCGC TGGGCTGCCTGCTGCGACCAGGG

20 Ordered Data Spatio-Temporal Data Average Monthly Temperature of land and ocean

21 Data Quality What kinds of data quality problems? How can we detect problems with the data? What can we do about these problems? Examples of data quality problems: Noise and outliers missing values duplicate data

22 Noise Noise refers to modification of original values Examples: distortion of a person s voice when talking on a poor phone and snow on television screen Two Sine Waves Two Sine Waves + Noise

23 Outliers Outliers are data objects with characteristics that are considerably different than most of the other data objects in the data set

24 Missing Values Reasons for missing values Information is not collected (e.g., people decline to give their age and weight) Attributes may not be applicable to all cases (e.g., annual income is not applicable to children) Handling missing values Eliminate Data Objects Estimate Missing Values Ignore the Missing Value During Analysis Replace with all possible values (weighted by their probabilities)

25 Duplicate Data Data set may include data objects that are duplicates, or almost duplicates of one another Major issue when merging data from heterogeous sources Examples: Same person with multiple addresses Data cleaning Process of dealing with duplicate data issues

26 Data Preprocessing Aggregation Sampling Dimensionality Reduction Feature subset selection Feature creation Discretization and Binarization Attribute Transformation

27 Aggregation Combining two or more attributes (or objects) into a single attribute (or object) Purpose Data reduction Reduce the number of attributes or objects Change of scale Cities aggregated into regions, states, countries, etc More stable data Aggregated data tends to have less variability

28 Aggregation Variation of Precipitation in Australia Standard Deviation of Average Monthly Precipitation Standard Deviation of Average Yearly Precipitation

29 Sampling Sampling is the main technique employed for data selection. It is often used for both the preliminary investigation of the data and the final data analysis. Statisticians sample because obtaining the entire set of data of interest is too expensive or time consuming. Sampling is used in data mining because processing the entire set of data of interest is too expensive or time consuming.

30 Sampling The key principle for effective sampling is the following: using a sample will work almost as well as using the entire data sets, if the sample is representative A sample is representative if it has approximately the same property (of interest) as the original set of data

31 Types of Sampling Simple Random Sampling There is an equal probability of selecting any particular item Sampling without replacement As each item is selected, it is removed from the population Sampling with replacement Objects are not removed from the population as they are selected for the sample. In sampling with replacement, the same object can be picked up more than once Stratified sampling Split the data into several partitions; then draw random samples from each partition

32 Sample Size 8000 points 2000 Points 500 Points

33 Curse of Dimensionality When dimensionality increases, data becomes increasingly sparse in the space that it occupies Definitions of density and distance between points, which is critical for clustering and outlier detection, become less meaningful

34 Dimensionality Reduction Purpose: Avoid curse of dimensionality Reduce amount of time and memory required by data mining algorithms Allow data to be more easily visualized May help to eliminate irrelevant features or reduce noise Techniques Principle Component Analysis Singular Value Decomposition Others: supervised and non-linear techniques

35 Feature Subset Selection Another way to reduce dimensionality of data Redundant features duplicate much or all of the information contained in one or more other attributes Example: purchase price of a product and the amount of sales tax paid Irrelevant features contain no information that is useful for the data mining task at hand Example: students' ID is often irrelevant to the task of predicting students' GPA

36 Feature Subset Selection Techniques: Embedded approaches: Feature selection occurs naturally as part of the data mining algorithm Filter approaches: Features are selected before data mining algorithm is run Wrapper approaches: Use the data mining algorithm as a black box to find best subset of attributes

37 Feature Creation Create new attributes that can capture the important information in a data set much more efficiently than the original attributes Three general methodologies: Feature Extraction domain-specific Mapping Data to New Space Feature Construction combining features

38 Mapping Data to a New Space Fourier transform Wavelet transform Two Sine Waves Two Sine Waves + Noise Frequency